{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 生成数据点\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y_true = make_blobs(n_samples=400, centers=4,\n",
    "                       cluster_std=0.60, random_state=0)\n",
    "X = X[:, ::-1] # flip axes for better plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xba9bac8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制出kmeans聚类后的标签的结果\n",
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(4, random_state=0)\n",
    "labels = kmeans.fit(X).predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');\n",
    "\n",
    "centers = kmeans.cluster_centers_\n",
    "plt.scatter(centers[:,0], centers[:, 1], c='black', s=80, marker='x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "kmeans算法相当于在每个族的中心放置了一个圆圈，（针对此处的二维数据来说）\n",
    "\n",
    "半径是根据最远的点与族中心点的距离算出\n",
    "\n",
    "下面用一个函数将这个聚类圆圈可视化\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n",
    "    labels = kmeans.fit_predict(X)\n",
    "\n",
    "    # plot the input data\n",
    "    ax = ax or plt.gca()\n",
    "    ax.axis('equal')\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "\n",
    "\n",
    "    # plot the representation of the KMeans model\n",
    "\n",
    "    centers = kmeans.cluster_centers_\n",
    "    ax.scatter(centers[:,0], centers[:, 1], c='black', s=150, marker='x')\n",
    "    \n",
    "    radii = [cdist(X[labels == i], [center]).max() for i, center in enumerate(centers)]\n",
    "    #用列表推导式求出每一个聚类中心 i = 0, 1, 2, 3在自己的所属族的距离的最大值\n",
    "    #labels == i 返回一个布尔型index，所以X[labels == i]只取出i这个族类的数据点\n",
    "    #求出这些数据点到聚类中心的距离cdist(X[labels == i], [center])  再求最大值 .max()\n",
    "    \n",
    "    \n",
    "    for c, r in zip(centers, radii):\n",
    "        ax.add_patch(plt.Circle(c, r, fc='#CCCCCC', lw=3, alpha=0.5, zorder=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果数据点不是圆形分布的\n",
    "\n",
    "kmeans算法的聚类效果就会变差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(13)\n",
    "# 这里乘以一个2,2的矩阵，相当于在空间上执行旋转拉伸操作\n",
    "X_stretched = np.dot(X, rng.randn(2, 2))\n",
    "\n",
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 引出高斯混合模型\n",
    "\n",
    "高斯混合模型能够计算出每个数据点\n",
    "\n",
    "属于每个族中心的概率大小\n",
    "\n",
    "在默认参数设置的、数据简单可分的情况下，\n",
    "\n",
    "GMM的分类效果与kmeans基本相同"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.mixture import GaussianMixture\n",
    "gmm = GaussianMixture(n_components=4).fit(X)\n",
    "labels = gmm.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');\n",
    "\n",
    "\n",
    "#gmm的中心点叫做 means_\n",
    "centers = gmm.means_\n",
    "plt.scatter(centers[:,0], centers[:, 1], c='black', s=80, marker='x');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得到数据的概率分布结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.    0.469 0.    0.531]\n",
      " [1.    0.    0.    0.   ]\n",
      " [1.    0.    0.    0.   ]\n",
      " [0.    0.    0.    1.   ]\n",
      " [1.    0.    0.    0.   ]]\n"
     ]
    }
   ],
   "source": [
    "probs = gmm.predict_proba(X)\n",
    "print(probs[:5].round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "编写绘制gmm绘制边界的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "def draw_ellipse(position, covariance, ax=None, **kwargs):\n",
    "    \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    # Convert covariance to principal axes\n",
    "    if covariance.shape == (2, 2):\n",
    "        U, s, Vt = np.linalg.svd(covariance)\n",
    "        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n",
    "        width, height = 2 * np.sqrt(s)\n",
    "    else:\n",
    "        angle = 0\n",
    "        width, height = 2 * np.sqrt(covariance)\n",
    "    \n",
    "    # Draw the Ellipse\n",
    "    for nsig in range(1, 4):\n",
    "        ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n",
    "                             angle, **kwargs))\n",
    "        \n",
    "def plot_gmm(gmm, X, label=True, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    labels = gmm.fit(X).predict(X)\n",
    "    if label:\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "    else:\n",
    "        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n",
    "    ax.axis('equal')\n",
    "    \n",
    "    w_factor = 0.2 / gmm.weights_.max()\n",
    "    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n",
    "        draw_ellipse(pos, covar, alpha=w * w_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在圆形数据上的聚类结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, random_state=42)\n",
    "plot_gmm(gmm, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在偏斜拉伸数据上的聚类结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n",
    "plot_gmm(gmm, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 将GMM用作密度估计"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GMM本质上是一个密度估计算法；也就是说，从技术的角度考虑，\n",
    "\n",
    "一个 GMM 拟合的结果并不是一个聚类模型，而是描述数据分布的生成概率模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "非线性边界的情况"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 构建非线性可分数据\n",
    "\n",
    "from sklearn.datasets import make_moons\n",
    "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n",
    "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果使用2个成分聚类（即废了结果设置为2），基本没什么效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm2 = GaussianMixture(n_components=2, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm2, Xmoon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果设置为多个聚类成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm16, Xmoon, label=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里采用 16 个高斯曲线的混合形式不是为了找到数据的分隔的簇，而是为了对输入数据的总体分布建模。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 利用分布函数的生成模型\n",
    "\n",
    "生成新的，与输入数据类似的随机分布桉树（用于新的数据点）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**用 GMM 拟合原始数据获得的 16 个成分生成的 400 个新数据点**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xnew = gmm16.sample(400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xnew?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.91802434,  0.4264853 ],\n",
       "       [-0.79114795,  0.70198326],\n",
       "       [-1.02085389,  0.22850745],\n",
       "       [-0.8498637 ,  0.46316015],\n",
       "       [-0.75870888,  0.67907014]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xnew[0][:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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M3ieVr0eRS9S3O0PMvvh6KQ1grD92qgRkE13UXI/jbV2q4LcFUsUETJ3iomlVI02r5qTcLNewGq+hUGSLMu9kiJWI1GR81V6qKl3s2NU6Zgm/dH49TavmjCsKrrfRuGS+j1++/X7W2R/1SCdKtpwx2wQHuGlhA9ubFhEMRyxvlufCm0qhsIJS+hli9sV3O+2Ehscr5eWLpvHSvnfGhf7vabnInpaL1CfZcI08SFwOR0p7so24b3ql16nrwqiHChKyhsflYOn8et1NcICTZ7sJhiMp3UITB/hcelMpFGZkrPSFEHbg+8Ay4mkMH5ZSto203QT8fcLpq4GtwCGgFTg5cvxFKeV3M5VhMjH7QoeGo3jddsA2pij41vXzeOKpXxp+ptEmX/JGYzxZWIy9LRd0c7/U13h49ONLafBV4nTYRjYHr64WjAYCFSRknaZVcwyVfuLM3KpvfjoDhEKRDdnM9LcCXinlGiHEauDbwMcApJTHgA8BCCE+AVyUUv5cCNEEPCel/OPsxC4MEr/QXX2BMW2a+eW2JTO4b6RerFWPnFQRsQ67PZ7mIBYziBptoHF69ejvyasFvYFABQmlR12Nl3oLM/N0gtNU8JYiH2Sj9NcBPweQUh4UQqxKPkEIMQX4GnD7yKGVwAohxF6gHfgTKeUloxv4fJU4nfmd4TQ0VKc+KYFH711J70CQR7/9+jjFD9B2oZdp06rwup1MqfLg9TgZCg7rfNJV/P0BHG4XDdOmpLx3dZWXgycv0dkzxLTaClYvmcmDW27A4Ri/R9+YdG0gNIy/L4ivxoPXPfmWvnT7frJZu2w2O/ed1Tk+i8ZZteOON447Mp7Jei7F1veJFLPskH/5s3mjaoDehN8jQginlDJRoz0E/LuUUvNbOwUckVLuEkJ8Cvge8HGjG/j9g1mIlz6ZBkrEZ/DjFT5AZ88QZ97tYrqvkh27WlMqfIjPFCOhsCVZtq69ljtvmYPD7SISCuNxOejuvmJZdifQ3zvEZIe3FGOQzZY1cxkcCiUkXIvPzLesmZvV36IFZ2nPc6Ipxr7XKGbZYUKDswzbslH6fUDiJ9uTFD7Apxir1HcDmiZ/Efh6FvcvGKwmTbPi2w3p23A9LgcN06YU9ctfjGimm8/eXcGZd7uyjqBVwVmKfJDNm9QM3AUwYtM/kdgohJgKeKSUiSWI/hm4e+TnDwNHsrh/weB02Kj06qcvrvQ6cTpsKV08bUlFuYuRbIqfFzNet5PpvkpLCt+sj1RwliIfZDPTfxHYJIQ4QNxD8AEhxBeANinlTmAR8G7SNV8CnhZC/CFwBXg4i/sXDM/vbjN0i3yvfYDnd7dx94b5Jql8PXzunmU01FYUpZeGmqGmJlUf5SLVtUJhhYyVvpQyCvx+0uFTCe1vEvfwSbzmHeCOTO9ZiFgx2xw+1c6W2641dMlbIRpobKiaKBEnHKvlHsuZVH2kgrMU+UJNw7LESmRuz0CIJ546RDQW48MrZ4+W0Ct2cw6o9AFWsNJHVZUuPG79mbwKzlLkksn30ytyUoXka/RcCbH7yAWaVjXyjUduLZl86mqGmhqzPuruC3D2Qi+HZbthziYVnKXIJWqmnyXpJkY7Kjvo6BkqCYUP5tlA1Qw1jlkf2Wzwtz86xt5jxkXvw8MRItHc51pSlCdK6eeAbRsX0LSqEZ8FBdfdH+SJpw7x2JMH2bGrtei/zGaDnpqhxjHro2gMYqCbTkNj77FLPPfa6YkRTlF2KKWfAzR/7a8+eDO1Ve6U55eaO5426JXSXkWuSewjG/HCNelw4MRltT+iyAnKpp9DqivdrFo8PWUGzERKwR0v18XPS5HEPjp7oZe//dGxtK4PhCJc7rrCNTNqJkhCRbmgZvo5ZtvGBcyZbt39MrmYRjGjZQNVCt8Yj8vBvNlTM6qK9sqh91KfpFCkQCn9HDMciY3WnrWC2uwsPzKtinb6fI8y8SiyRin9HJNuRS212VmejLHxW7Tvd/cHS2ZVqJg8lNLPMWbueV63nfoaj9rsVIza+L/xyK08dNd1lq6xAa8cOlf0Hl+KyUVt5OYYj8tBpdelG6zVUFvJl+9bqTY7FaN4XA5unF+PjbhXlxnRGOxpuYjDYVfpLRQZo2b6OSYYjnBlKKTb1u4fJBKNqs1OxSiRaJSdze+kVPiJqPQWimxQSj/H9A4E8ffrK/1gOMqOV1WQjeIqz+9u47UjF9K6ppQ8vhT5Ryn9HGNm0wc49Ru/mqUpAGsZWvVILMxTjvULSpl8PFNl088SrbSdZqP3uBwsnuuj+eRl3fN7BoIqCZkCSN/TS2PZwnpe2HtG1S8oIRLrLXT1BamtcrN84TS2b1qU82eqlH6GJBfF8FW7WXxNHds3LeTeTYs40tpOIDTey0L55Ss0rGRo9bjsTPG66BkIjtbgjcViqn5BiZFcb6FnIMSelou0Xejj8ftX5VTxK6WfITtebWVPy9XMiN39IQ6cvMwR2c4qMZ0Vi6Zx4GT7uOvKxS8/eQWkGI8WpGWWtmP9sllj0lsAPPbkQd1zSyGlRzliZuZ7r32AHbtOc99HRM7up5R+mkSiUXbsOm2YCjcYjuqadtxOG+uXzSp5v3xVOjE9tm1cQCwWY//xSwTDV1eGXredtTfOHO03zRzY7h80zc2vTIfFR+9A0HS1d6y1k3vuWJCzwVwp/TR5fncbe46m520BEBqOYbPZSl7xqdKJ6eGw2/nUJsHHP7SAjp4hQuFh3C6nYb1kM5OQzQavvPke25sWlvx7VioEQsOEwhFqq9z0DOh7/fVcye0+oFL6aZCpt4XGkVPtJb38Nuuf/ccvsXX9PCo96pXTw+NyWKqTbGYSisZgz9ELOOw2NcAWMMFwhO6+ALsOv8fb7/rp8A/hdhnn4qjL8T6g+gamQabeFhr+gVBJL7/N+icQivDcq6089NHr8yxV6bFt4wIikSh7j13ULb7S0trJltuuZSg4rPZUCohkD51EgmHj8Lxc7wNmrPSFEHbg+8AyIAg8LKVsS2j/B2At0D9y6GOAC9gBVAAXgQeklIOZypBvrNbDNcJX5S5pz52pVR581W66DYLTTp2LxygoJZQdDrudO1Y08nqL/r5SV1+AJ54+RO9ASO2pFBDJpk89PC47FR4nvVdC1I14a+V6HzCbmf5WwCulXCOEWA18m7hi11gBbJZSdmoHRgaCHVLKZ4QQXwI+C3wnCxnyihVvCzNuWljanjsel4PF19RxwCBGwd+vYhSyRZstHpXtpqkbNPuwtqcyFBjm05tFSb9/hYxV03B4OMpX7luG2+WYsFVaNkP/OuDnAFLKg8AqrWFkFbAQ+IEQolkI8WDyNcDPgKYs7p9TguEIlzqvpIyES06Jm07Zu+NnukqiLq4Z2zctxOvWf1FVjEL2aLNFo9WUEc0nL/OVH7xR8u9foWLVNOx22ambWjGh+bmymenXAL0Jv0eEEE4p5TAwBfge8HeAA9gjhDicdE0/MNXsBj5fJU7nxM5MIpEoT7/8NgdPXqKjZ4iG2gpWL5nJg1tuwOGwEwgN4+8L4qvx4HXHu+uzdy/jctcgEOOn+87yyi/PjfvcplWN9A2FOfT2+6PHtFlXZYWbR7bemPO/paGhOuefmQkfufUadu47O+742mWzaJxVa3hdocifCfmQPRAa5viZLsP2uhqPqWLp7g8Zvn+q7yeW6qkVNPgqaPcPmZ4XCEX5r8PnJ0Q/aGSj9PuAxN62jyh8gEHgu5q9Xgixm7jtX7tmaOT/HrMb+P0Tb+7fsat1jLmm3T/Ezn1nGRgMYrfZxvib37RwGjHgrdOddPcF8bgdxGLxWZOWGreu2s0KMZ2t6z/IE08d0r1n81sXufOWOTkdyRsaquno6E99Yh7YsmYug0MhWlo78fcHRiNJt6yZOypjcvBWIcmfLvmSvd0/SIeB0rABf7j1Bv7xpbdT7jklv3+q7/PD0vn1lkzDudAPZgNhNkq/GdgC/HjEpn8ioW0R8CMhxAriJqR1wA9HrrkLeAa4E9iXxf2zxszOduDEZQKhq6aerr7guGyIie2affVKID7u9Q6EDGddWpbEUrVtGxVKjyeTusKuI+c53tY5Jnjrj+5ZPtliFzxVlS48bseY906jrsbL7IZqls6vHxMprkepv3+FyraNC4hEYynjfCb6+WSj9F8ENgkhDhCfaDwghPgC0Cal3CmE+DfgIBAG/kVK+bYQ4hvAD4UQjwCdwPYs5c+KVC6GmRAMR9l1+DyRaMzQ06fUbduJs/jpvkoGg2H++aeSU7/pHmeLTjR5bV177eQIXCS8tO8dw/dSc+vbuHJ2SqVf6u9foeKw29l885yUSt9X7ZnQ55Ox0pdSRoHfTzp8KqH9W8C3kq55H/itTO+Za7J1wTTjeFuX4ayrVPPv6CWhm1Lhpr1nkKBO8rlEDp68lHOTVylhtir1uh1sXT8PgN0WcvOX6vtXDEyt8lCfQudcCYR5Ye+ZCXOzLWvHXc0FUw8jDxSrdPcHuP2mWaOePuVQF1fzLOnqCxIjvnH4XvtASoUP0NkzpAqDmGC2Kg2FIwwMhgiGI6YbvV63vaTfv8nEah58M52jEQjFrQXP724zPS9Tyj4iV/sCJG86xmKxtCsaJRKLwfd+cpwVYjpfe+gWBgZDJR0dmW2Kimm1FcrkYILZqrS2Km4OSOUW+D+2r+CaGTUTKWbZkUmCwUSd090XAPTrI09U1tSyV/qJm44Ot4tIKIzH5WAwOEzziUu6OfGtornIQeknG8s2RcWS+crkYIZZYOBgcJgX9p5h6/p5hgNDfY2XGfVT8iFqWZFJgsFEndN1Jcxf/NMB3fMmakO3rM07iXhcDmZOmzKqeAYGQ5bMElYoh0LWqcpEmuF1O/i9rUtyLFHpoQUGJpseA6EIuw6f56V9Zw1NB8qOn3vMVrdWvvMelwNxjc/wezNRG+5K6Rug5ZHJBeVQyNqKrdKIdUtnMqUiN31dyjjsdu7eMJ8pXv0FektrJ1vXf7Cs9pEmE7PVrdXvvNftzPtAXfbmHSNS5ZFJh3JxkUveH6mt8jClwjWywaW/aop7nnwwn2IWNakUzcBgWDdGQpF7zPZZEr/zyYGIib+D8b7iRA3USulz9aFUT60Y8/vHPzSPo60dGfvsa5TL0lovKAvgV+92870XTuheE/c8CedTzKLGqqLxuBwq+GqCMdtnWb5oGk6HjR27Wsds8lZ6XVwZCuHvj2dAXbtsNlvWzM3rQF3WSj95573BF69WlPhQfFUeLnWnlw7C63YQCkcmfMQuVDwuB/VTvWNyh9tt6OZ+L5dVUK5IpWjKYXJRSJjN0vU2eRMH666+IDv3nWVwKMT2pkV5G6jLWuknP5TkZEjaA3LYwemwExqOUlftpdLr5L32gXGf53U7WLd0JlvXzyt5F81UJPetnsIHpagyId/mAIUxZilHrLow57ugfdkq/XQeSiQaXxW4HTZumOdje9NCfvL62TG268XX+Ni+aSGVHhdAWZcFNOtbu01LTKcUVaYYKRrF5JE8S0/HhTnfuZDKVjNl4lceisT4xbFLnLnQxx9uXaJK0hlg1rexGPzZJ29i3uypqs+yJFNzQPLGoiL3pJPixVftpcLjpN0/mJdnUrZKP5u8Oxc6rvCVJ39JfUL0neIqZn1bV+Mdp/CD4QjvXurD779CQ22FUkQThFH0qMpwmnvSqbJX6XXy9WfetBzRmy1lq/SzLX0I1qLvyhGrm42RaJTnXjvNgYTIZ6/bwdobZ/DJDy9UNV1zjFH0qMpwOjFok8GjsoPu/qvODNr/ddUeaqs9nL3YN3pNPnRK2X6rguEIdyyfzR0rZo8Gskz3VVBVkf44WA4Rt+mSWFbSKEjo+d1t7D5yYUyqi0AowmtHLkxYsqlyxWyf5eDJS+r9nQC0vZcl8+uAq84M2v/Xf9BHj0EA10TqlLKb6estcZfOr6dp1RyuafTx6Lf3MDA0nPqDElBFKcaTarOxfzDE4V+3G17f0tqRV4+GUqd3IGhoyuzwD+m+v8r2nx2DwWGefeUUhwze8wMnLht6tU2kTik7pa+3xN3TchGHw84906ozShqmfM2NSd5s1Abdw6fa6bliXNy7uz+oBtIcMrXKg9dt100g6HE7xry/mWSOVFxF67/5Y4+nAAAgAElEQVT9xy+aJmw0UvgwsTqlpJ9gco7rVAmSKr3OjJKG3bSwXs2ELKINuj0Dxgof4vZONZDmGpvu0UAowo93nyYSjSuo5LoImp1ZmdysofVfNhl6JzJ+pSRn+kYzlTuWzzbNWzIYGM5oc9dkwFYkkE5sxPJFDWogzSG9A0GCJulEtNXu3Rvmm06MlMnNnGzrStRWuVm1ePqEegSWpNI38lJIVbfWV+MZV+DAZpA+IJG3TnfxiQ9F1JchBWZ2ZQ2Py866pTOVG2yOseKi3NLawe1LZ6bMHKlMbsZkU1fCV+Xhqw/eTHXlxGacLTnzjtlIq9Wt1WP5oml43c7RDchvPHIr3/zsajYsn53ynuWQOjkXVFW6cLvMX7mv3LeST20SynacY5wOG5Vel+k5XX1BsNnynt+9lLBSV6KxQb+YzcrFDROu8KEElX6q1LN3rGhkzvQq7CPmTbsN5kyv4uMfmjfmXG0DcnvTwhHXQ+MHqb4M1nhp3zuEDFIsQ9yO36BmkRPC87vbdPNFJWK3wdQpblWIJQtS1d1uWtXIY59ZOak1D0rOvJMq9eyelgtjXv5oDN5rH+Anr5/l0XtXjrsm0fXwX1+Ruvn11ZchNVZsnVMqXKofJwCrduZoDIaCwyqhW5bo1ZVIzs2lV6I1X2Sk9IUQduD7wDIgCDwspWxLaP888MmRX/9TSvk1IYQNOA+cHjn+hpTyzzOW3ACzaNCl8+s43tape11LayeBkLF/vsfl4IG7FlPpdaovQwZYsXUOBsIEw5FxhSbUQJAdVu3MmseUSuiWHVb7z+Ny0DBtCh0d/XmVL9OZ/lbAK6VcI4RYDXwb+BiAEGIe8CngVuKOLfuEEC8Cg8BRKeWW7MU2x2imcsfy2bzeclH3mu7+AJe7BrnSP2T4kNSXIXOsbCT6+4N09wXY03JB+YjnEKt5plaIsR5TqhBL7imEyUymSn8d8HMAKeVBIcSqhLb3gN+SUkYAhBAuIACsBGYLIfYAQ8DnpZTS7CY+XyVOZ2Yd8+i9KwmEhvH3BfHVePC6nQRCwzT4KsblzYd49scvfu8XBEIRGmorWL1kJg9uuQGHQ1/RNGYk1cTS0FA92SKYsnbZbHbuO2vYPq22gua33zfMD/PI1hvzIWZGFHrfhyPmLmhul53fvet6fCPV44qJQuv7SCTK0y+/zcGTl+joGaK+xsOCOT6meBy0nO6kuy9IfY2XW5fM4Pe23ph3+TNV+jVAb8LvESGEU0o5LKUMA50j5py/AVqklK1CiBnAN6WU/y6EWAc8C9xsdhO/P72KVXo4gf7eIbQFlNnoOhSM+zG3+4fGVLQpBhoaqvO+TEyXj6xq5L9++a5h0Mp11/j45clLum3Nb13kzlvmFOTKqtD7vn8wRL9J9DNAKBzl0b/by8rFxbWqKsS+37GrdczEpbM3SGfv2L3Arr4A/3ngXU69282ff3pFzvvbbCDJ9E59QOKn2qWUowZxIYQX+LeRc/5w5PBh4P8CSCn3E5/164cIThDBcIQrQ+YvfyIqkVpuGRgMETSJUly1qMHQ9tzVF6C7LzBRopU071zssxRA6B9QkbfZEgxHOCqNc0olc/ZiHztebZ1AicaTqdJvBu4CGLHpj1a9HlHk/xd4S0r5Wc3MAzwBfG7knGXAOSllXoNZeweC+PutK33lf59bzHyY7XY43NqBr9rYT3nX4fcmSrSSJBKNsmNXKz98xdSKOg412cmc3oEg3WnoGIDmE5cZDKaX5DEbMlX6LwIBIcQB4DvA54UQXxBC/Dfim7wbgDuFEK+P/FsD/DWwQQixF/g74P7sxU8PK4ETiSj/+9xi5sMcjcLeYxdNA4jeePv9vH45ih0tMt3fn97ERU120iMxx1eFxzkaA2SV0HCU5/I428/Ipi+ljAK/n3T4VMLPXoNL/59M7pcr0i2covzvc8+2jQuIRKLsPXZRN71Fn4ntORCKsOO/JA9vuWECJSwNsskBoyY71tDL8SXm+lKmbdHj1Dn/qLvyRFMcuzU5ZNvGBcyZXmV6jt0GdyyfpfzvJwCH3c7mW+YSM/hi9A2GTa8/erpDmR4skE0OGDXZsYZeNtIDJy/jdaevVrv7gnlbXZWd0h+OxBgMmCuWGLD5lrlF48FQbKRrZkskEIrSkQOvrlInnT6228E2CekAiplss2kmM7XKnbfVVcmlYUiFlRlQnVreTihZ1ye25dXpqyhJp49jUfizT940rmC9whgzPZJJHv3lC/O3uiq7qayVGZBa3k48Wg1dXwaD69QpE5+JsBSwYsoEaPBVKIWfJmZ6JN0pyZzpVWzflL94oLJS+sFwhO6+ABUe/QVOhcfB2iUz2Lp+nm67IndoKS2++uDN1Falp8SHlAePJayYMgFWL5mpFH6amHmipdrHtdvii1VflYe7bruWx+9flVdTclmYdxJ32Y3yj1R6HEypcHHg5GVOnfOrfC95oroyXinIqqmnvkaVUbSKFVOm1+0gGosRiUbVu54mejm+li6o51hrO/4B48E2GoPV10/nM3deR+Os2qJJuFZUJFfS0mMwGGFwJA2Dlu8FKJo0DMXMto0LqKxw81+//A0Bk5J+oMoopoOVRGuBUISf7n+HQCCs3vU0MUrAaLPB7iMXTK89da4nT1KOp+SH9mx22VVkYn5w2O08svVG/va/r2XtkhnU13iwEZ+Fet2OSSk0UQqYmSCSOXKqg/7B9CJJFXG0bKTaZCQaTb2R2zsQmrQAuJKf6Wfjr6xqguaXSo+Thz56/Zj0s8Ckp6ItZu5afQ37jl0kOGyuiPwDQZ54+tBoUW5l6kmfeNqL0/zimH7SwETqaibPQ7Dklb7VXOJ6qMjEySE5j7sadNNH28c6fKo9pcLX6BkIKbNmFjy/u409R83NOhqT6SFY8sN5qiVufY3X0K1NuW4qihVtH6tnIH2TjTJrpo9VM7Kvyj3pZsqSn+mDwS77/DqaVs2hrsaL02HjR6+d5sDJ90fdAb1uu/JqUBQl2UaLKrNm+lg1I9vTzcY2AZSF0rdS5tBms43x/w6Eouw+cgG7zaaWugVGIZScK2Sy2ccCZdbMBKtm5ELwDCwLpa9hVPPTbGbU0trJ3RvmK+VSAOhlNVTxFOPJZh8LlFkzE9JNLaLplclAfVMwnxmp3OKTj5avfMeu0+OyGqpKT+Ox6qrpddvZsHwm030Vyi02B2ipReprPNhsmEaaT6ZeKauZfiKJJoIKj5OpVW7dTS+11J08kiOpjcyhR2UHty+bRUNthZqhjpC4j9VlUGYyEIricjj4P1/cyJl3u5S5LEfEYrF46vBYFLfLTig83ntqMvVK2Sn9ZBOBx+0AYoaZ8cTc2vwKqBjlR6+d5rWEyEaj4hTd/UEef+oQ9crcM0riPtbl7kH++tkjBHWUT0trJ6DcYnNBcuR/zxXjHFGTaUIrO6Wf/GCMwv697vgDeePkZaTKxZN3guEIzScup3WNZu6JxWJ8apOYIMmKC4/LQYXboTvbhLiZwd8XLD9FkGOsekzV13hZvmjapJrQykqDWX0wHqedQChCIBRRtuNJoqNnKGUeHiOaT1xWfuYJmKUB9lV78WVY0EZxle6+QMqNc1+Vh8fvX8X2pkWTOnksK6Vv5cEAhhGMKmgljxjVU7RAIBSho2coh8IUN2Ybu8sXTcPrVvP8bNl1JLXXTu+VYEGkBS+rp73r8HtZXa+CVvJHg68Sr9ueURUiIKtBoxTRC1CcbDNDqRAMRzje1pnyvEJxCslY6Qsh7MD3gWVAEHhYStmW0P4I8FlgGPiGlPKnQohpwA6gArgIPCClzEvB02A4wvEzXZbO9boduqaFQnlo5YDH5eC2G2emTFFrhHpOY7ESoKjIDKvBcIUS/5CNeWcr4JVSrgG+BHxbaxBCzAD+BFgLbAa+KYTwAI8DO6SU64EW4oNCXrDyYKb7Kmha1cjaG2foti9Wnjx55d4PL6RpVSN11fFUy3XVHj60YhaNDVNSXlsIy+hCJDkNsCJ7UpVgra/xFFT8QzbmnXXAzwGklAeFEKsS2m4BmqWUQSAohGgDlo5c81cj5/xs5OfvZCGDZcyiFOuqPXzunmVct6CB/t4hItEoNpttdCnsdsXdOptVVa28YjQ73bGrlfMdVwyvU9W1FPnELBr3tiUzuG+zKKhBNhulXwP0JvweEUI4pZTDOm39wNSk49oxQ3y+SpzO3HXW2mWz2bnv7Ljj626azfLrZwLgbagG4NF7VxIIDfNPLxzntYS9AM2Tp7LCzSNbb8yZbLmgYUT2YsVM/saR/3sHghxN4YF1JTjMzw69x4NbbsDhyM/AXMp9X+gUgux/dM9yKivcHDx5ic6eIabVVrB6yUxL72C+5c9G6fcBidLaRxS+Xls10JNwfCjhmCF+f27N/VvWzGVwKDRuM2vLmrl0dPTT0FA9pl5lMBzhWGu77mc1v3WRO2+ZAxRGkY9k2YuNVPIn5odPlS44EIywc99Z3u8a4P47rwMm9hkVa99rUenzr62nv7c4vZ0mq+/1kv5tXXstd94yZ8zx7m7jFSlMnPxmA0k2Sr8Z2AL8WAixGjiR0HYI+EshhBfwANcBJ0euuQt4BrgT2JfF/dPG6maW9kBD4YjhPkB3X4BnX5GcOudXyb/ygJU6x8n88lftvPnrdlzOeCi8ekZxkqPSG3wVLJ1fX/b9YoVUSf+MkjoWEtko/ReBTUKIA4ANeEAI8QWgTUq5UwjxD8SVuh34ipQyIIT4BvDDEc+eTmB7lvJnhNGDiUSi7NjVOuaBegzcBj1uB80nr0aMFkLK1FIlm/zw0Rij6QfUM4qTPIC2+4dUv1gkue+K8Z3KWOlLKaPA7ycdPpXQ/iTwZNI17wO/lek9J5qnX3573ANNF5WKOfdkmx8+mXJ+RiqNeOZk0neFWPuhrIKzzAiGIxw8qV/Q2Ot2UOlx0jMQxFftRcyt5Y2T+nlhVABX7qmqdOExiJ3IhHJ+RlbSiJdjv6QiGI5w9kKv4UQwue8KufaDUvoj9A4EDUP3Q+EIX75vJW6nfdQVUJ7z674AKoAr97z4i7M5U/hQ3s9oapXHcAB1uxxl2y9GJCtvu00/22vyO1XIZiC1azPC1CoPDbUVum2+ai8NtRWjQS2pcpkUyjKuFMgk22Yq1DNSKSqs8qPXxhbuMUrvnfhOpTIDTXb+LqX0R/C4HKxeMlO3TU9JXK2S41VVhyaQbLJtJmKjfJ+RVnlMsy8b5TMKhiKqSlwC/YMh9r+lb/IF43eq0CvxKfNOAg9uuUHXj19PSahcJnkiB4nTbDb4s203MW/21LJ6Rnp25aULplFX7aa7f3ysQ11N+Zq9EkmMCTHKuAvw6CeWIub6xr1TZtH/hWBaVEo/AYcjfUVeDH65xUzW2TaBumpv2Sl80Lcr7zl6gTnTq3SVfjmbvRK9bF7Ye8ZSTEhdtb5+MEvLUAh9rJS+DkqRFw5m2TaNNtWSKYQvWr4xsysPBsLcsXwWx8904+8PMK32anBWuTEYHOa5V1vHBFleCYRTXuewQ91U/T1AKOxU1krpKwqeez+8ELvNxlHZgb8/iK/aw7IF9bx1psvUf78QStNNFuZ25SCbb5nLPRsXFn0ahkzRTDj7j18cs4q0GpsTicJL+84aeuIUsvlXKX1FwaP3BeodCPJ6y0XDa76wbRkLG2sL5ouWb6zYlbUVrdftpPgyB2VHJmk9kmlp7eD2pTNpMElVXYhWA+W9oygaEnPBm+Uwr6/xlrXCh9QlEsu5b7JJ65FIV1+Qx59+k8eePMiOXa1EopnvO+UTpfQVRUkqpQaMuimWK8qtWJ9cp/XQAq+e392W+uQCQJl3FEWL3mbZTQvricZiPPbkwYILf883hWxXnkzMTF/ZUCy5i5TSVxQtekrthb1neK1Aw98ni0K0K08mZi6V2VAsuYvKa+qjKEkSlVohh78rCodtGxdwx4rZ2Gy5+8xCCLyyglL6ipLBzFbb3R/g7IXeMYo/MT2Borxw2O1svnlOLgK+RymWDXJl3lGUDGa2WhvwNz86Rn2Nh2ULp2EDjp3upLsviK/azeJr6ti+aSGVHlfe5VZMDlOrPIYpKVIxs66SYDgymm69mOJBlNJXlAxmtlotcrerLzguure7P8SBk5c52trBmiUzaFrZSF2NtyhmbYrM8bgcrBDT07bt11V7ePyBm4HCqI+dLkrpK0qKRI+e7v4ANqylagAIhCLsOXqBPUcvUF/GXj/lxLaNC4jGYjQfvzRaVjMVK0TDqJIv9E1bPdTbrCgpNI+ebzxyK3+27SbLCj+ZRN9rZfsvXRx2O5/eJPj7P1nPrddNT3m+121n6/p5eZBs4lAzfUVJ4nE5mDd7KvVZ+mPvP36pIEveKXKLx+Xg4S3XUz3Fzb5jFw1TKofCUQYGQ1R6ild1qjdXUbKYRe1aJRCKjFZNKrbIS0V6aKvEb/7+atwufdVYLG6ZZiilryhp9FIRbFw5mw+vnI3Xndnmm/L5L21qq7zcvmyWbluxuGWakdEaRQhRATwLTAf6gc9IKTuSzvkbYN3IPX4gpXxSCFEHtAInR057UUr53UyFVyhSYZaK4Ldvn8+zr0gO/fr9tGz/xRJ5qcgcK/nwEwuvFNNAkKlh6g+AE1LKrwohPgk8BjyqNQoh7gAWSCnXCCE8wNtCiJ8AK4DnpJR/nK3gCkU66KUiqPQ42br+gxz81ftpfZav2kuFx0m7f7Dol/oKfcwmC3plKItprydTpb8O+NbIzz8D/iKp/Q3g2MjPMcABhIGVwAohxF6gHfgTKaVh5WGfrxKnM78jaENDdV7vl0uKWXbIr/yB0DD+viCNs2qZ7qug3W+9iMjUKjd/+a9H6OgZoqG2gtVLZvLglhtwOAr/C29EMb87Ey17Y9LvT750YlwZyl2Hz1NZ4eaRrTem/fn57vuUSl8I8RDw+aTD7wO9Iz/3A1MTG6WUASAghHABPyRu3hkQQpwCjkgpdwkhPgV8D/i40b39/kHLf0guaGiopqOjOMtJFLPskD/59WZplV7rUbhTvA7OXuwb/b3dP8TOfWcZHAoVbUK3Yn538i17MByh+a3xpTsBmt+6yJ23zEnL1DNR8psNJCmVvpTyKeCpxGNCiP8AtE+tBnqSrxNC+ICfAK9LKb85cng3oGnyF4Gvp7q/QpFL9IqFd/UFR8Pq/f1xTx0jBgP6G7jFklZXcZVMbPLmZSiLY68nU/NOM3AXcAi4E9iX2Diy0fsa8G0p5b8lNP0z8ALwY+DDwJEM769QpI1ZxaRL3YPUVbu59foP8OtzfnoH9POxGA0IxfKFV2Rnk7dShrLQyVTp/yPwQyHEfiAEbAcQQnyL+Ox+LTAPeEQI8cjINQ8AXwKeFkL8IXAFeDgL2RWKtEhVMam7P8TBX71PY8MUQ6Vvt+mndSiWL7xCf7WXWHPBbAVglt+pWNw5M1L6UspB4BM6x7848uMh4DsGl9+RyT0VimyxWjFpMDBMY8MUzndcGdc2u6GK99oHxh0vli98uWO22mtp7SASiXL8TJfpCsCKO2chU7yxxApFmnhcDpYumMaeo/obcRo9A0E+d88y/t+db3Ox4wox4jP8WdOm8KVPL+fFX7wz5gu/dtkstqyZm58/QjGOdGzzHf5Bw0G/qy/InpaLY37Xq7pW7GUoldJXlBV3LJ+dUun7qr3sabnAhYSZfjQG5zuu8I1njvCVz6wc84VvnFVbtN4vxUwkGuXJl07Q/NaFlLb5RDu+EUamO6NN+mItQ1m8jsUKRQbsOZo6d/rS+XUcb+vUbbvUPcif/u9mXth7hvqpKuf+ZPL87jZ27js7LjfSM/95alyaDM2Ob2baM4rK7uoLcKFzvEmvWFFKX1E2BMMRjp/pMmz3uOw0rWqkadUc0w3fYDiqEq9NAokprs1s880nL/OVH7zBjl2tRKJR03MT8RgkWQP4q385whNPHyI0PJyx/IWCMu8oyoZU3jtf+vRKrvlANcFwhNoqD/4B8w1fbdmvmFg008xR2U53f4i6kfKWqTyxNHt808pG03M1bCZV0qMxeK99gL/8l6N87cFb0v8jCgg101eUDZr3jh71NV5m1MXtsx6Xg5sWTUv5eZpvviIz9IrT6B177rXT7Dp8frSWrVbe0mZBe7W0dlLhcRo+90RC4Qi3LZlBXbXb8JwLHQP0D6ZfU7eQUDN9RdmQjo/19qaFtJ3v1XXP1KiZ4qbCpJiGmVdJsWZozAV6wVHJxerrajwsXTCN25fOpPm4fnquqIXqht39AXqvhAyfeyK+ai/3bRbI33Tz9z85oX/PGJxvH+C6a+tS37xAscViGdaTywMdHf15FU7lIJk88p97Z7yPtZ7Hx45XW2k+eZmQQf3U+hoPa5fNZsuauaPXm0V8AgWXoTGXfW9loHvl0LkxrpETTV21m5sWNYwMKl109QV0z2ta1cj2pkX0D4b4/Pf2627s2m3wnT9eR3Wl8WogHSYw946hrUop/QSKWXEWs+wwOYmzrM60B4PDPPdqK6fO+Q29PzSFAbBjV6vurLJpVTxfo1HbZCVsy7TvE/vQ6bBZHuhsBq6RE03Tqkbu3jCf7r4Au46c53hbl+HA/8TTh3RXeXOmV+XUpj8ZSl+ZdxRlSTo+1pUeJw999Hr6B0N89ek3dTd4Ezd1jTxFjsoOjPYKiylhm1Gm0kQlmRjYBGMHuomcZxr52sPVPp5ZP4X7PiII3mE88H/ld1fwl/9ylAsdA0Rj8c+d3VDFV353xcQJnyeU0lcoLDIUHKbHYOM2cVPXOAuj8aZvMSVsM8pUqkdLawf5tCZM91VwuVu/NkJyH5sN/G6nk689eAv9gyHOtw/QOL0qZyadyUYpfYXCIlOrPPiq3aNeJInUVMY3dd0uh0kWRg82G0WdoTEYjnBUtls+v7s/OKEze416ndVGMpn0cXWlu6g3bfVQLpsKhUU8LgdTKvRnez1XQnz9mTd5Ye8Zblqo7+65QjSwfFGDbptewjY998VcEwxHuNR5xdI9ItEoz74idQc9I+qqPYYukMZe8elx25IZPH7/zQwGwqbnqaR4cdRMX6GwSDAcMVUsmh1748rZNK1qNM3CmNi2dEE9dyyfTTAcweNy5KUG65h79AfxVcUDnrZvWkilR7+S2PO722g+eTmt+1R6XYi5tbqb126XneULpyHP+fEPjO9XzT7vsENEx3nKYbdx523X8rHbrqGrN2AagHXbkhlFkwVzolFKX6GwSKqIXo23TnfxjUduNczCqGVo7O4LsOvwexxv6+T1oxdGlXssFuO1I1eTwqWT792I5GuS7fJawNPR1g7WLZ05OsBo11V4nJZSGSRzZSjM1vUfBGD/8UsEQomBWFEO/qodo9LCG26axeZb5lJV6eKF18/QcrqTnoEQU6e4uO4aH5/eLLimsY6Ojn7TtNn1NR7u2yyKomh5PlBKX6GwiNV8/IkbhkYbhR6Xgz0tF3RT+Xrd+or8qOwgEo1xvK3TdAWQypVy6YJpvHVaX4EHQhF2HT5PLBbDZrONXje1yk2PQWEZM3oGggwMhrl7w3xaWjvGKH2N5Fm81+0YM/AA3Ld5MfdszLS4SYMy6ySglL5CYREzxZKIlQ1DsyRgeooR4puiiWmhtUEiEo2x+eY5VFW6eGnfOyldKVOllgZoPnF5jBypFL4N/VKSWl9YXSUBTPE6uXvD/HEzc83bRtvrSO7jYi9uki+U0lco0iBRsRhFdlrZMExHCWoY+aDvbbnAnqMX8LodYxS1mSulmT87GA88Rhh9lNYXVldJEHdt1XNf1dvrSIyGLvbiJvlCKX2FIg0SFYtmk3/7XT+dPUNpzSwrPM60TSZGSlo7no6iznVErDaIaP/XVXtYIa5G5FpdJYHxSkkvPmDnvrMMDoXGRDMXa3GTfKGUvkKRAR6XIx7ZuXkx1VMrOPNul6WZZeJsNR2FP7thCoHgsKWZshXqazzcMK+O/W9d0h0AjDxmjNA+Q/t/2cJp49JKJJtf3C6H7kBl5L5qXNu2eKKZCwGl9BWKLPG6nZZnlsmzVasEgsMjGT1zo/QrvS5OnukynPE7HXYiVtJYGnC8rYvgHXEX1MSN5UTzy9U9iNQ2eDNzWDFFMxcCGSl9IUQF8CwwHegHPiOl7Eg6ZydQD4SBISnlnUKIBcAzxE2AJ4H/LqXM/M1SKIoIqxWc9OjqC1I7JTObzJzpVQwGhkcVa6XXaRq5ChAejnLbkhnIcz34+wPUTEnPFOXvD9DdF2BPywXdeANNQVu1wZvtCRRLNHOhkOlM/w+AE1LKrwohPgk8BjyadM4C4AYpZeKb+nfAY1LK14UQ/wR8DHgxQxkUiqIik81bjdoqN70Wla7bZWd4ODpm5jwciY3623/9mTdTfoaWW16TW7vOqnmpZoqbV948xy+OXc2FnxxvoGHFBp9OLQSFOZkq/XXAt0Z+/hnwF4mNQogPALXAy0KIWuCvpZQ/BVYCexOu+whK6SvKhHQ8WJJZvnAax890pbzW7bLz159dQygcGTNzdthhuq+Sdv+gpYEnUZFqCtnqRizEXTz3v6Vf/CRTG7yeS+baZbPYsmZuWp9T7qRU+kKIh4DPJx1+H+gd+bkfmJrU7ga+DXwXqAOahRCHAFvCzF/vujH4fJU4nfkdwRsaqvN6v1xSzLJDcctvVfa1y2azc99Zy59b4XHy4Zvn8PB/W8LTL7+d8tqmm+ey8IPjc/8EQsP4+4I0zqqlwVdBu18/E+V0XwWrl8zkwS034EgKlf2je5ZTWeHm4MlLdPYMMa22gltumAHAobcvj/tMo/2C7r4ADreLhmlTTP8WPR69d+Xo3+Kr8eB1F/+2ZL7f+5Q9JqV8Cngq8ZgQ4j8ATdJqoCfpssvAP0kph4F2IUQLIIBE+73edWPw+wdTiZdTirkQSTHLDsUtfzqyb1kzl57+oTFmDz1uWdzAR9d+kIbaCjwuB93dV9iyZi6DQy6gZ5kAAAfVSURBVKFx6Qw05kyv4rfXXTtGFqPc93rctmQG920Wo/fTY+vaa7nzljnjbPCbVsw2rDWQjMftIBIKZ/W8nUB/7xDeIn5vYEKLqBi2ZZqMohm4a+TnO4F9Se1NwI8BhBBVwBLg10CLEOJDJtcpFCWNw27n/t+6jsYG81nuYdnBnqPncTqu5qJ02O1s27iA1Td8AI/z6lfX47SzYfksHr9/1bgoVs1bqKsvSIy4Xf299gHmTK+ivsaL3Raf3TetauSBuxZbMrloNvjEc81qDSQTHo5m5Rk0UeQjq2khkOna6B+BHwoh9gMhYDuAEOJbwE+klD8TQmwWQhwkPrv/spSyUwjxp8CTQgg38UHgJ9n/CQpF8fHYZ1bytacPc6lbfzUbjcGelos4HPYxm57P727j9aT6ssHhKC6HfZzCN/MWGgwM8/j9qxgKDjP/2nr6e/XNPVZJZ78iEo2x49XTPPzR61Oem48C8vnIalpIZKT0pZSDwCd0jn8x4efP6bS3AhsyuadCUUq4nU4ef+BmvvyDg6YVtRI3PdMNUErl2z4UHGa6rxKv20m2BoZ0Im4BTv3GP5pKWo98KmK9SF89L6NSofSGMYWiSPC4HKwU+kVVNBLLMFoJUEpEm33rMRG+7ds2LqBpVeOo2cjjMlYvPQPBcfImomeW2nX4PM/vbhs9J50CMEakGkhL0dRT/FvfCkURs23jAiLRGHtbLuh6uyQq53QDlPLt256c8MztcvDlH7xBIDTefm826KRSxFvXz+OlfWdHC8DUVWe+CijHSF8101coJhGH3c59HxFsuGmWbnuictaUeKrzEkmefdfXeGla1Tih6Ya1jd7aKg/rlqb+u5JJpYife7X16iogpr8KsEq+V0OFgJrpKxQFwPZNi3A47Cnz0KSbM36y0w1nkuPebEVTW+Xh1Dm/7nWZBH2VY6SvLZaPUvUZ0tHRn1fhysVXvBApZvlzKbtVb5VcerXko+/TlXfHrlZdRXzbkhm8cfKybv5+uw3+6vdWp22OubppPH5gmmjvnQn00zesO69m+gpFAWE1F3yx5YxPV16jFcLW9R9EnvPnNPHaZK+G8o1S+gqFouAwU8QTZY4ptoE0U5TSVygUBYueIla1cLNDKX2FQlFUJK4CHG4XkVC4pM0xuUa5bCoUiqLE43Iwc9oUpfDTRCl9hUKhKCOU0lcoFIoyQil9hUKhKCOU0lcoFIoyQil9hUKhKCOU0lcoFIoyoqBz7ygUCoUit6iZvkKhUJQRSukrFApFGaGUvkKhUJQRSukrFApFGaGUvkKhUJQRSukrFApFGaGUvkKhUJQRZZ9PXwjx28AnpJTbddoeAT4LDAPfkFL+NN/yGSGEqACeBaYD/cBnpJQdSefsBOqBMDAkpbwz74KOlccOfB9YBgSBh6WUbQntBdvfYEn+fwDWEn8eAB+TUvbmXVAThBC3Av9LSvmhpONbgMeJ9/3TUsonJ0E8U0xk/wLwEKC9/5+VUso8i2eIEMIFPA1cC3iIv9s7E9rz2vdlrfSFEN8FNgPHdNpmAH8CrAK8wH4hxKtSyvHFOSeHPwBOSCm/KoT4JPAY8GjSOQuAG6SUhRKBtxXwSinXCCFWA98GPgZF0d9gIv8IK4DNUsrOSZEuBUKILwL3AVeSjruA7wA3j7Q1CyFellJezr+U+hjJPsIK4HellEfyK5VlPg10SSnvE0LUAy3ATpicvi93884B4spTj1uAZillcGS21gYszZtkqVkH/Hzk558BTYmNQogPALXAy0KI/UKIj+ZZPj1GZZZSHiSu4DUKvb/BRP6RVcBC4AdCiGYhxIOTI6IpZ4Df0Tl+HdAmpfRLKUPAfmB9XiVLjZHsACuBPx95z/88jzJZ5d+Bv0j4fTjh57z3fVnM9IUQDwGfTzr8gJTyeSHEhwwuqwESl+b9wNQJEC8lBvK/z1X59GRzE5+JfheoIz6DOCSlbJ9IWVOQ3KcRIYRTSjms0zZp/W2CmfxTgO8Bfwc4gD1CiMNSyuOTIKcuUsoXhBDX6jQVfN+byA7wI+D/AH3Ai0KIjxaSaVBKOQAghKgGfkJ8Va6R974vC6UvpXwKeCrNy/qA6oTfq4GenAmVBnryCyH+g6vy6cl2GfinEYXULoRoAQQwmUo/uU/tI/LptU1af5tgJv8g8F0p5SCAEGI3cdt/wSh9E4qh73URQtiAv9f2ToQQ/x+wHCgYpQ8ghJgDvAh8X0q5I6Ep731f7uYdMw4B64UQXiHEVOLLsJOTLFMizcBdIz/fCexLam8CfgwghKgClgC/zpt0+ozKPGITP5HQVuj9DebyLyK+D+EYsdOuA47mX8SM+DWwUAhRJ4RwA7cDb0yyTFapAU4KIapGBoCNQEHZ9kdMrf8F/A8p5dNJzXnv+7KY6afDiCdAm5Ry54g3xj7ig+NXpJSByZVuDP8I/FAIsR8IAdsBhBDfAn4ipfyZEGKzEOIgEAW+XAAbjC8Cm4QQBwAb8EAR9Teklv/fgIPEvaX+RUr59iTKmhIhxHagSkr5g5G/4xXiff+0lPLC5EpnTpLsXwb2EPeoek1K+Z+TK904vgz4gL8QQmi2/SeBKZPR9yq1skKhUJQRyryjUCgUZYRS+gqFQlFGKKWvUCgUZYRS+gqFQlFGKKWvUCgUZYRS+gqFQlFGKKWvUCgUZcT/D+FMCPvopxUMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew = gmm16.sample(400)\n",
    "plt.scatter(Xnew[0][:, 0], Xnew[0][:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 需要多少成分？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "作为一种生成模型，GMM 提供了一种确定数据集最优成分数量的方法。\n",
    "\n",
    "- 赤池信息量准则（Akaike information criterion)  [AIC](https://en.wikipedia.org/wiki/Akaike_information_criterion)\n",
    "\n",
    "- 贝叶斯信息准则（Bayesian information criterion) [BIC](https://en.wikipedia.org/wiki/Bayesian_information_criterion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(1, 21)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(Xmoon)\n",
    "          for n in n_components]\n",
    "\n",
    "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n",
    "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('n_components');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "观察可得，在 8~12 个主成分的时候，AIC 较小"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm12 = GaussianMixture(n_components=12, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm12, Xmoon, label=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
